Voltera系统在平稳正态激励下的离散表示

Volterra响应系统是一种十分有用的数学模型，本着重讨论了在平稳正态激励下Volterra响应系统的离散化问题，即将激励过程{x(t)，t∈[-T，T]}离散化，利用Kac-Siegert的思想，以Neal提出的表示定理为基础，直接地给出Volterra响应系统的离散化的表示形式，由于它是由激励过程直接地表示响应系统的形式，因而在实际计算Volterra响应时有广泛的实用价值。     

求在平稳正态激励下二阶Volterra响应的最大值分布的两种数值方法

是在输入x(t)作用下的二阶Volterra响应,其中核函数(或脉冲函数)h(τ_1,τ_2)是[0,T;0,T]上的一个实对称的连续函数,激励{x(t),-∞相似文献   

线性随机参变振动的谱分解法

本文是[1]文的一个发展.考虑如下的随机方程:(t)+2β?(t)+ω₀2Z(t)=(a₀+a_lZ(t)).I(t)+c,激励I(t)和响应到Z(t)都是随机过程,并设它们相互独立.如[1],设I(t)=a(t)I0(t),a(t)是已知的时间函数,IO(t)是平稳随机过程.本文考虑了以上随机方程的谱分解形式,数值求解方法以及一些特殊情况的解式.     

Volterra核函数法在轴承滚珠磨损中的特征提取及应用

针对滚动轴承滚珠磨损故障特征难以提取的问题,提出一种基于多脉冲激励法下的Volterra级数核的求解算法.该方法是一种非线性系统模型的“交叉”诊断法,利用轴承系统输入输出的采样信号,建立Volterra非线性辨识系统模型,并运用多脉冲激励Volterra低阶核求解算法,将得到的低阶核通过时域和频域进行对比来判断轴承当前所处的运行状态.该文以无心车床主轴轴承为例进行实验验证,并与传统的小波分析法对比得出:多脉冲激励法能够方便准确地提取轴承的故障特征,该方法对此类故障的诊断具有一定的借鉴意义.     

具有分数导数型本构关系的粘弹性柱的动力稳定性

研究简支的受轴向周期激励的粘弹性柱动力稳定性,柱的材料满足分数导数型本构关系.建立了描述粘弹性柱动力学行为的弱奇异性Volterra积分-偏微分方程,利用Galerkin方法将其化归为弱奇异性Volterra积分-常微分方程.利用平均化方法的思想给出了粘弹性柱运动稳定状态的存在性条件.给出一种新的计算方法,克服了存储整个响应历史数据的困难,并给出了数值算例,计算结果与解析方法的结论比较吻合.     

从离散速度模型到矩方法

为了求解动理学方程,我们通过研究一维情形下的离散速度模型,发现通过对离散速度点使用自适应技术可以直接得到Grad矩方程组.作为一个统一的认识,矩方程组可以看作是对离散速度点自适应的离散速度模型,而离散速度模型可以看作是取特别形式的"矩"的矩方程组.这使得我们可以在一致的框架下来理解离散速度模型和矩方法,而不是将它们对立起来.为了建立这样的一致框架,最近在[2]中发展的正则化理论是根本性的.     

一类激励-抑制型时滞神经网络模型解的收敛性

本文考虑一类激励-抑制型时滞神经网络模型解的收敛性.利用分析的方法并结合平面系统的几何特性,得出初值φ=(ψ,Ψ)∈R2,在响应区间[a,b]的端点a和b处不振动时,解(z(t),y(t))→(0,0)(t→+∞).     

大型对称二次束部分极点配置的多步法

正1引言在结构动力学中,利用有限元技术,对具有n个自由度的阻尼线性系统进行离散化,得到如下的二阶常系数线性微分方程[1]Mx(t)+Cx(t)+Kx(t)=f(t),(1)其中M,C,K∈R~(n×n)分别是对称的质量矩阵、阻尼矩阵和刚度矩阵,且M正定,x(t)∈R~n是位移向量,t表示时间,f(t)是外作用力或控制向量.当f(t)=0时,对(1)进行分离     

小波变换及其应用(续二)

(五 )离散小波变换正交小波基上面我们介绍了连续小波变换 ,但在实际问题及数值计算中更重要的是其离散形式 (在作具体数值计算时 ,连续小波的参数 a,b必然要离散化 )。对确定的小波母函数ψ( t) ,取定 a0 >1 ,b0 >0　　令ψmn( t) =am20 ψ( am0 t-nb0 ) ,　 m,n∈ Z ( 5.1 )这里 Z表示全体整数所构成的集合 ,我们称 ψmn( t)为离散小波。对于函数 f( t) ,相应的离散小波变换为 :Cf( m,n) =∫∞-∞f ( t)ψmn( t) dt,m,n∈ Z ( 5.2 )　　我们知道对连续小波 ,由 Wf( a,b) ,a,b∈ ( -∞ ,∞ ) ,a≠ 0可唯一确定函数 f ( t) (反演公式( 3 .…     

基于哈尔小波函数的非线性随机It?-Volterra积分方程的数值解

正1 引言随机积分方程在工程、生物学、海洋学、物理学等领域有着广泛的应用,用其对随机现象进行建模变得越来越重要.由于系统的多样性和不同噪声影响,多种形式的随机方程都用于系统建模.其中,随机Volterral积分方程广受关注.然而,许多随机Volterra积分方程不存在精确解,因此对随机Volterra积分方程寻求较高精度的数值解是有意义的.目前,随机Volterra积分方程有不同的数值解法,如正交基法[4,6-11,13,14,16-18],Wash级数法[2,3],多项式法[1,5,12,15,19,20]等.     

二阶Volterra系统对平稳正态激励的统计响应的表示定理的数学证明

1974年,Neal根据Kac和Siegert的思想,给出了一个在电子工程、海洋工程、建筑工程、航空工程、自动控制的随机振动中有重要应用的二阶Volterra非线性系统对平稳正态输入的统计响应的表示定理.1984年,Naess对此定理又给出了一个数学证明.经过研究后发现,他们对定理条件的叙述都是模糊的,而且其数学证明都是有问题的.本文重新讨论了这个表示定理,给出了明确的定理条件及严格的数学证明,为它的广泛应用奠定了理论基础.     

On the representation of nonlinear systems with gaussian inputst †

An arbitrary nonlinear system with input a Gaussian process, which is such that its output process has finite second moments, admits two kinds of representations: the first in terms of a sequence of deterministic kernels and the second in terms of a single stochastic kernel. We consider here the identification of the sequence of deterministic kernels from the input and output processes, the representation of the system output when its input is a sample function of the Gaussian process or another equivalent Gaussian process, and the relationship of the sequence of kernels mentioned above to the Volterra expansion kernels when the system has a Volterra representation.     

Direction of Hopf bifurcation in a delayed Lotka–Volterra competition diffusion system

This paper is concerned with a delayed Lotka–Volterra two species competition diffusion system with a single discrete delay and subject to homogeneous Dirichlet boundary conditions. The main purpose is to investigate the direction of Hopf bifurcation resulting from the increase of delay. By applying the implicit function theorem, it is shown that the system under consideration can undergo a supercritical Hopf bifurcation near the spatially inhomogeneous positive stationary solution when the delay crosses through a sequence of critical values.     

Extremes of Volterra series expansions with heavy-tailed innovations

In this paper, we look at the extremal behavior of Volterra series expansions generated by heavy-tailed innovations, via a point process formulation. Volterra series expansions are known to be the most general nonlinear representation for any stationary sequence. The so called complete convergence theorem on point processes we prove enable us to give in detail, the weak limiting behavior of various functionals of the underlying process including the asymptotic distribution of upper and lower order statistics. In particular, we investigate the limiting distribution of the sample maxima and the corresponding extremal index. The study of the extremal properties of finite order Volterra series expansions would be highly valuable in understanding the extremal behavior of nonlinear processes as well as understanding of order identification and adequacy of Volterra series when used as models in signal processing. In fact, such extremal properties may suggest a way of finding the order of a finite Volterra expansions which is consistent with the nonlinearities of the observed process.     

Multiple Wiener-itô integral expansions for level-crossing-count functionals

Summary This paper applies the stochastic calculus of multiple Wiener-Itô integral expansions to express the number of crossings of the mean level by a stationary (discrete- or continuous-time) Gaussian process within a fixed time interval [0,T]. The resulting expansions involve a class of hypergeometric functions, for which recursion and differential relations and some asymptotic properties are derived. The representation obtained for level-crossing counts is applied to prove a central limit theorem of Cuzick (1976) for level crossings in continuous time, using a general central limit theorem of Chambers and Slud (1989a) for processes expressed via multiple Wiener-Itô integral expansions in terms of a stationary Gaussian process. Analogous results are given also for discrete-time processes. This approach proves that the limiting variance is strictly positive, without additional assumptions needed by Cuzick.Research supported by Office of Naval Research contracts N00014-86-K-0007 and N00014-89-J-1051     

Entropy meaning of summability of the logarithm

We consider the mutual relations between the concepts of sets of uniqueness for analytic functions, the loss of entropy in nondetermined stationary linear filters, Szegö's theorem and the familiar condition of summability of the logarithm. The goal of the paper is to give the physical meaning of these mutual relations. Here we take the concept of linear stationary filter and loss of entropy in it as basic. In the first part of the paper the account is given for the case of discrete time, and in the second part we give the method of passing to continuous time. To this end we introduce the concept of stationary sampling system. This is a sequence of functions from L²(), which transforms any stationary Gaussian process with continuous correlation function into a stationary Gaussian process with discrete time. Such systems can be described in terms of the Fourier transform. Laguerre systems where z is a fixed point in the upper half-plane, play a special role among all sampling systems. If z=i, then is a classical Laguerre function on the line up to a multiplicative constant. Laguerre sampling systems allow one to give the entropy meaning to the values of the harmonic extension to the upper half-plane of the logarithm of the spectral density of the processTranslated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 73, pp. 152–187, 1977.     

ON LOCAL CONTINUITY MODULI FOR GAUSSIAN PROCESSES

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一类Lotka—Volterra型捕食与被捕食系统的Flip分岔

本文利用中心流形定理和映射的分岔理论,研究了一类离散的捕食与被捕食系统的Flip分岔的存在性与稳定性,并给出了数值模拟的结果。     

Functional limits of empirical distributions in crossing theory

We present a functional limit theorem for the empirical level-crossing behaviour of a stationary Gaussian process. This leads to the well-known Slepian model process for a Gaussian process after an upcrossing of a prescribed level as a weak limit in C-space for an empirically defined finite set of functions.We also stress the importance of choosing a suitable topology by giving some natural examples of continuous and non-continuous functionals.     

Approximation of stationary solutions of Gaussian driven stochastic differential equations

We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to the SDE. Then, we end the paper by some specific properties of this stationary solution. We show that, in contrast to Markovian SDEs, its initial random value and the driving Gaussian process are always dependent. However, under an integral representation assumption, we also obtain that the past of the solution is independent of the future of the underlying innovation process of the Gaussian driving process.